Matrix Log of Triangle A051731=A054525^-1

[Paul D. Hanna]

Seqfans, 
       How would one submit the following triangle of UNIT FRACTIONS 
that is aerated with many ZEROS? 
 
The triangle is the MATRIX LOG of triangle A051731=A054525^-1, and 
is closely related to the MoebiusMu function.  
   
Below I define triangles A051731 and A054525, and give a FORMULA for the
matrix log
in terms of sequence A100995.  
  
Any suggestions on the best way to submit to the OEIS?  
Thanks, 
      Paul
---------------------------------------------------------------------- 
 
* Triangle A051731 is defined by: 
A051731(n,k)=1 if k|n, 0 otherwise. 
   
* The matrix inverse of triangle A051731 is triangle A054525 defined by: 
A054525(n,k) = MoebiusMu(n/k) if k|n, 0 otherwise. 
  
* The matrix log of triangle A051731 is defined by:  
T(n,k) = 1/A100995(n/k) when k|n and A100995(n/k) is non-zero, T(n,k) = 0
otherwise. 
  
* Sequence A100995 is defined by: 
"If n is a prime power then its exponent, else 0."  
  
The matrix log of triangle A051731 begins:
0;
1,0;
1,0,0;
1/2,1,0,0;
1,0,0,0,0;
0,1,1,0,0,0;
1,0,0,0,0,0,0;
1/3,1/2,0,1,0,0,0,0;
1/2,0,1,0,0,0,0,0,0;
0,1,0,0,1,0,0,0,0,0;
1,0,0,0,0,0,0,0,0,0,0; ...
 
Which consists entirely of unit fractions and zeros.
 
If we list only the denominators of the unit fractions of the non-zero
entries, 
and leave zero entries alone, we get the triangle defined by:  
*  T(n,k) = A100995(n/k) when k|n, 0 otherwise. 
    
But what about at all those zeros ... 
Being a matrix log, I would hate to leave out any zeros ...
  
Row#: Row elements;
1: 0;
2: 1,0;
3: 1,0,0;
4: 2,1,0,0;
5: 1,0,0,0,0;
6: 0,1,1,0,0,0;
7: 1,0,0,0,0,0,0;
8: 3,2,0,1,0,0,0,0;
9: 2,0,1,0,0,0,0,0,0;
10: 0,1,0,0,1,0,0,0,0,0;
11: 1,0,0,0,0,0,0,0,0,0,0;
12: 0,0,2,1,0,1,0,0,0,0,0,0;
13: 1,0,0,0,0,0,0,0,0,0,0,0,0;
14: 0,1,0,0,0,0,1,0,0,0,0,0,0,0;
15: 0,0,1,0,1,0,0,0,0,0,0,0,0,0,0;
16: 4,3,0,2,0,0,0,1,0,0,0,0,0,0,0,0;
17: 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
18: 0,2,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0;
19: 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
20: 0,0,0,1,2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0;
21: 0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
22: 0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0;
23: 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
24: 0,0,3,0,0,2,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0;
25: 2,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
26: 0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0;
27: 3,0,2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
28: 0,0,0,1,0,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0; 
29: 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
30: 0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; ... 
   
END